Engineering Mathematics I

Course Title: Engineering Mathematics I

Course No: SH 112

Nature of the Course: THEORY

Semester: 1

Full Marks: 100

Pass Marks: 45

Credit Hours: 3

Course Description

This course provides fundamental mathematical concepts required in engineering. It covers differential calculus, integral calculus, two-dimensional analytical geometry, and vector algebra. Students learn techniques for solving mathematical problems involving derivatives, integrals, curves, conic sections, and vectors, which form the foundation for advanced engineering and computational studies.

Course Objectives

The basic objective of the course is to provide a sound knowledge of differential calculus, integral calculus, two dimensional analytical geometry and vector algebra. After learning the course one may enhance the fundamental concepts on Mathematics and able to study the further courses of the subject which are more applicable in Engineering.

Course Contents

1. Differential Calculus

1.1. Higher Order Derivative

Review of limit, continuity and derivative

Successive differentiation of some special functions

Higher order derivative and Leibnitz rule for derivative of product of two functions

1.2. Mean Value Theorems

Rolle's Theorem and Lagrange's Mean Value Theorem (Statement and proof), their geometry and applications

Cauchy Mean Value Theorem (statement and proof) with applications

Taylor's and Maclaurin's infinite series for real valued functions (without derivation) with examples

1.3. Indeterminate forms

L' Hospital rule and its application to evaluate the limit of a function

1.4. Asymptotes

Types (horizontal, vertical and oblique) and equation of asymptotes to the curve represented by algebraic polynomial equations

1.5. Curvature

Concept of curvature and its radius

Radius of curvature of Cartesian, polar, parametric and pedal curves

2. Integral Calculus

2.1. Indefinite Integrals

Evaluation of indefinite integrals by using standard methods (methods of substitution, partial fraction and integration by parts)

2.2. Definite Integrals

Definite integral with properties

2.3. Beta-Gamma function and Reduction formulae

2.4. Integration by summation method of some standard functions

2.5. Improper integrals and Cauchy principal value

2.6. Techniques of curve sketching (Cartesian and polar form)

2.7. Application of integration

Arc length

Area between curves

Volume of solid of revolution

3. Two Dimensional Analytical Geometry

3.1. Review of Standard equation of parabola, ellipse and hyperbola in Cartesian form, equation of tangent and normal to those curves and problems related to tangent and normal only

3.2. Polar equation of conic section and their classification in terms of eccentricity

4. Vector Algebra

4.1. Review of scalar and vector product of two vectors and their geometrical interpretation

4.2. Scalar product of three and four vectors and their geometrical interpretation with properties

4.3. Vector product of three and four vectors, Reciprocal system of vectors of three non-coplanar vectors

Reference Books

1.E. Kreyszig, Advanced Engineering mathematics, Wiley-Eastern, Publication.
2.N. P. Bali, Dr. Manish Goyal, A text book of engineering mathematics, Laxmi Publication (P). LTD.
3.Thomas George B. and Finney. Ross L., Calculus and Analytical Geometry, Pearson Education

Notes:

This syllabus follows the official B.E Computer curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authorative.

Mathematics I